Monk and Inversions
Tag(s):

## Data Structures, Easy

Problem
Editorial
Analytics

Monk's best friend Micro, who happen to be an awesome programmer, got him an integer matrix $M$ of size $N \times N$ for his birthday. Monk is taking coding classes from Micro. They have just completed array inversions and Monk was successful in writing a program to count the number of inversions in an array. Now, Micro has asked Monk to find out the number of inversion in the matrix $M$. Number of inversions, in a matrix is defined as the number of unordered pairs of cells $\{(i, j), (p, q)\}$ such that $M[i][j] \gt M[p][q]\space \&\space i \le p\space \& \space j \le q$.
Monk is facing a little trouble with this task and since you did not got him any birthday gift, you need to help him with this task.

Input:
First line consists of a single integer $T$ denoting the number of test cases.
First line of each test case consists of one integer denoting $N$. Following $N$ lines consists of $N$ space separated integers denoting the matrix $M$.

Output:
Print the answer to each test case in a new line.

Constraints:
$1 \le T \le 100$
$1 \le N \le 20$
$1 \le M[i][j] \le 1000$

SAMPLE INPUT
2
3
1 2 3
4 5 6
7 8 9
2
4 3
1 4

SAMPLE OUTPUT
0
2

Explanation

In first test case there is no pair of cells $(x_1, y_1)$, $(x_2, y_2)$, $x_1 \le x_2 \space \& \space y_1 \le y_2$ having $M[x_1][y_1] > M[x_2][y_2]$, so the answer is $0$.
In second test case $M[1][1] > M[1][2]$ and $M[1][1] \gt M[2][1]$, so the answer is $2$.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala 2.11.8, Swift, Visual Basic

## CODE EDITOR

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## This Problem was Asked in

Challenge Name

CodeMonk (Arrays & Strings)

OTHER PROBLEMS OF THIS CHALLENGE
• Data Structures > Arrays
• Algorithms > String Algorithms
• Algorithms > String Algorithms
• Data Structures > Arrays